Runner A is initially 4.6 km west of a flagpole and is running with a constant velocity of 4.8 km/h due east. Runner B is initially 7.4 km east of the flagpole and is running with a constant velocity of 6.4 km/h due west. What will be the distance of the two runners from the flagpole when their paths cross?
To find the distance of the two runners from the flagpole when their paths cross, we need to determine the time it takes for them to meet and then calculate their distances from the flagpole at that time.
Let's first determine the time it takes for the runners to meet. We can use the equation:
Time = Distance / Velocity
For Runner A, the distance is 4.6 km (because they are initially 4.6 km west of the flagpole) and the velocity is 4.8 km/h (because they are running due east):
Time for Runner A = 4.6 km / 4.8 km/h = 0.958 hours (rounded to 3 decimal places)
For Runner B, the distance is 7.4 km (because they are initially 7.4 km east of the flagpole) and the velocity is 6.4 km/h (because they are running due west):
Time for Runner B = 7.4 km / 6.4 km/h = 1.156 hours (rounded to 3 decimal places)
Since we are looking for the distance when their paths cross, we need to find the distance covered by each runner during the time it takes for them to meet. We can use the equation:
Distance = Velocity * Time
For Runner A, the velocity is 4.8 km/h and the time is 0.958 hours:
Distance covered by Runner A = 4.8 km/h * 0.958 hours = 4.6056 km (rounded to 4 decimal places)
For Runner B, the velocity is 6.4 km/h and the time is 1.156 hours:
Distance covered by Runner B = 6.4 km/h * 1.156 hours = 7.3824 km (rounded to 4 decimal places)
Now, let's determine the distance of the two runners from the flagpole when their paths cross. Runner A has covered a distance of 4.6056 km eastward from their starting point (4.6 km west of the flagpole) while Runner B has covered a distance of 7.3824 km westward from their starting point (7.4 km east of the flagpole).
To find the distance of the two runners from the flagpole when their paths cross, we add the distances covered by each runner to their starting positions with respect to the flagpole:
Distance from the flagpole = (Starting distance of Runner A from the flagpole) + (Distance covered by Runner A)
= (Starting distance of Runner B from the flagpole) - (Distance covered by Runner B)
= (4.6 km) + (4.6056 km)
= 9.2056 km (rounded to 4 decimal places)
Therefore, the distance of the two runners from the flagpole when their paths cross will be approximately 9.2056 km.